Do I need to inform insurer, if I have had paid to the third party for the damage?

[Rahul]

I have not accepted any liability? I have just paid for his damage.

But you have accepted that you were at fault at the time of accident and offered/paid the amount in lieu of going to the insurer. And this is not documented anywhere, if that driver (third party) go to his insurer, what proof you have to show that this was agreed between you and him.

So when ever you are doing any such activity, always inform your insurer (also take insurer opinion).